Question

Use the given data to find the minimum sample size required to estimate the population proportion.

margin of error: 0.007; confidence level: 99%; from a prior study, (p) hat is estimated by 0.255.
a. 25,708
b. 23,137
c. 14,895
d. 180

Answer 1

To calculate the minimum sample size required to estimate a population proportion given the margin of error, confidence level, and an estimated population proportion from a prior study, a specific formula must be used

The correct answer is A.

Step-by-step explanation:

To find the minimum sample size required to estimate the population proportion with a given margin of error at a specified confidence level, we can use the formula:

n = (Z^2 * p*(1-p)) / E^2

Where:

• n is the sample size,
• Z is the Z-score corresponding to the confidence level,
• p is the estimated population proportion,
• E is the margin of error.

For the question given, we have:

• Margin of error (E): 0.007
• Confidence level: 99% (which corresponds to a Z-score approximately = 2.576)
• Estimated population proportion (p): 0.255

To calculate, the formula translates to:

n = (2.576^2 * 0.255 * (1 - 0.255)) / 0.007^2

Calculating the above expression gives a sample size that is closest to A.